19.2 Electric Potential in a Uniform Electric Field

A negatively charged massive particle is dropped from above the two plates in the figure into the space between them. Which best describes the trajectory it takes?

1. A rightward-curving parabola
2. A leftward-curving parabola
3. A rightward-curving section of a circle
4. A leftward-curving section of a circle

Two plates are lying horizontally, but stacked with one 10.0 cm above the other. If the upper plate is held at +100 V, what is the magnitude and direction of the electric field between the plates if the lower is held at +50.0 V? -50.0 V?

1. 500 V/m, 1500 V/m, down
2. 500 V/m, 1500 V/m, up
3. 1500 V/m, 500 V/m, down
4. 1500 V/m, 500 V/m, up

Consider three parallel conducting plates, with a space of 3.0 cm between them. The leftmost one is at a potential of +45 V, the middle one is held at ground, and the rightmost is at a potential of -75 V. What is the magnitude of the average electric field on an electron traveling between the plates? (Assume that the middle one has holes for the electron to go through.)

1. 1500 V/m
2. 2500 V/m
3. 4000 V/m
…

A certain electric potential isoline graph has isolines every 5.0 V. If six of these lines cross a 40 cm path drawn between two points of interest, what is the (magnitude of the average) electric field along this path?

1. 750 V/m
2. 150 V/m
3. 38 V/m
4. 75 V/m

The electric field strength between two parallel conducting plates separated by 4.00 cm is $7 . \text{50} \times \text{10}^{4} \text{ V}/\text{m}$. (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be at zero volts. What is the potential 1.00 cm from that plate (and 3.00 cm from the other)?

(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength for air ($3.0 \times \text{10}^{6} \text{V}/\text{m}$) if the plates are separated by 2.00 mm and a potential difference of $5.0 \times \text{10}^{3} \text{V}$ is applied? (b) How close together can the plates be with this applied voltage?

Membrane walls of living cells have surprisingly large electric fields across them due to separation of ions. (Membranes are discussed in some detail in Nerve Conduction—Electrocardiograms.) What is the voltage across an 8.00 nm–thick membrane if the electric field strength across it is 5.50 MV/m? You may assume a uniform electric field.

Find the maximum potential difference between two parallel conducting plates separated by 0.500 cm of air, given the maximum sustainable electric field strength in air to be $3.0 \times \text{10}^{6} \text{V}/\text{m}$.

An electron is to be accelerated in a uniform electric field having a strength of $2 . \text{00} \times \text{10}^{6} \text{V}/\text{m}$. (a) What energy in keV is given to the electron if it is accelerated through 0.400 m? (b) Over what distance would it have to be accelerated to increase its energy by 50.0 GeV?